If the courier delivers the package to you damaged, then yes, when signing for the delivery you must record that it has arrived broken.
If the breakage is not detailed, the transportation company will not accept the claim.
Once you have it, take as many photos as possible so that you can see the damage to the goods, the outer packaging (box) and the inner packaging (protection) that you have used. It is also essential that one of the images shows the label of the transportation company. By doing so, we will be able to speed up the claim. :)
You must keep the original packaging as it was received, so the transport agency can assess your goods and decide whether compensation will be given.